/*
 * Copyright (c) 1997, 2013, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
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 */

package java.awt.geom;

import java.awt.Shape;
import java.awt.Rectangle;
import java.io.Serializable;
import sun.awt.geom.Curve;

/**
 * The <code>QuadCurve2D</code> class defines a quadratic parametric curve
 * segment in {@code (x,y)} coordinate space.
 * <p>
 * This class is only the abstract superclass for all objects that
 * store a 2D quadratic curve segment.
 * The actual storage representation of the coordinates is left to
 * the subclass.
 *
 * @author Jim Graham
 * @since 1.2
 */
public abstract class QuadCurve2D implements Shape, Cloneable {

  /**
   * A quadratic parametric curve segment specified with
   * {@code float} coordinates.
   *
   * @since 1.2
   */
  public static class Float extends QuadCurve2D implements Serializable {

    /**
     * The X coordinate of the start point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public float x1;

    /**
     * The Y coordinate of the start point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public float y1;

    /**
     * The X coordinate of the control point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public float ctrlx;

    /**
     * The Y coordinate of the control point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public float ctrly;

    /**
     * The X coordinate of the end point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public float x2;

    /**
     * The Y coordinate of the end point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public float y2;

    /**
     * Constructs and initializes a <code>QuadCurve2D</code> with
     * coordinates (0, 0, 0, 0, 0, 0).
     *
     * @since 1.2
     */
    public Float() {
    }

    /**
     * Constructs and initializes a <code>QuadCurve2D</code> from the
     * specified {@code float} coordinates.
     *
     * @param x1 the X coordinate of the start point
     * @param y1 the Y coordinate of the start point
     * @param ctrlx the X coordinate of the control point
     * @param ctrly the Y coordinate of the control point
     * @param x2 the X coordinate of the end point
     * @param y2 the Y coordinate of the end point
     * @since 1.2
     */
    public Float(float x1, float y1,
        float ctrlx, float ctrly,
        float x2, float y2) {
      setCurve(x1, y1, ctrlx, ctrly, x2, y2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getX1() {
      return (double) x1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getY1() {
      return (double) y1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getP1() {
      return new Point2D.Float(x1, y1);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlX() {
      return (double) ctrlx;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlY() {
      return (double) ctrly;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getCtrlPt() {
      return new Point2D.Float(ctrlx, ctrly);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getX2() {
      return (double) x2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getY2() {
      return (double) y2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getP2() {
      return new Point2D.Float(x2, y2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public void setCurve(double x1, double y1,
        double ctrlx, double ctrly,
        double x2, double y2) {
      this.x1 = (float) x1;
      this.y1 = (float) y1;
      this.ctrlx = (float) ctrlx;
      this.ctrly = (float) ctrly;
      this.x2 = (float) x2;
      this.y2 = (float) y2;
    }

    /**
     * Sets the location of the end points and control point of this curve
     * to the specified {@code float} coordinates.
     *
     * @param x1 the X coordinate of the start point
     * @param y1 the Y coordinate of the start point
     * @param ctrlx the X coordinate of the control point
     * @param ctrly the Y coordinate of the control point
     * @param x2 the X coordinate of the end point
     * @param y2 the Y coordinate of the end point
     * @since 1.2
     */
    public void setCurve(float x1, float y1,
        float ctrlx, float ctrly,
        float x2, float y2) {
      this.x1 = x1;
      this.y1 = y1;
      this.ctrlx = ctrlx;
      this.ctrly = ctrly;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Rectangle2D getBounds2D() {
      float left = Math.min(Math.min(x1, x2), ctrlx);
      float top = Math.min(Math.min(y1, y2), ctrly);
      float right = Math.max(Math.max(x1, x2), ctrlx);
      float bottom = Math.max(Math.max(y1, y2), ctrly);
      return new Rectangle2D.Float(left, top,
          right - left, bottom - top);
    }

    /*
     * JDK 1.6 serialVersionUID
     */
    private static final long serialVersionUID = -8511188402130719609L;
  }

  /**
   * A quadratic parametric curve segment specified with
   * {@code double} coordinates.
   *
   * @since 1.2
   */
  public static class Double extends QuadCurve2D implements Serializable {

    /**
     * The X coordinate of the start point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public double x1;

    /**
     * The Y coordinate of the start point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public double y1;

    /**
     * The X coordinate of the control point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public double ctrlx;

    /**
     * The Y coordinate of the control point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public double ctrly;

    /**
     * The X coordinate of the end point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public double x2;

    /**
     * The Y coordinate of the end point of the quadratic curve
     * segment.
     *
     * @serial
     * @since 1.2
     */
    public double y2;

    /**
     * Constructs and initializes a <code>QuadCurve2D</code> with
     * coordinates (0, 0, 0, 0, 0, 0).
     *
     * @since 1.2
     */
    public Double() {
    }

    /**
     * Constructs and initializes a <code>QuadCurve2D</code> from the
     * specified {@code double} coordinates.
     *
     * @param x1 the X coordinate of the start point
     * @param y1 the Y coordinate of the start point
     * @param ctrlx the X coordinate of the control point
     * @param ctrly the Y coordinate of the control point
     * @param x2 the X coordinate of the end point
     * @param y2 the Y coordinate of the end point
     * @since 1.2
     */
    public Double(double x1, double y1,
        double ctrlx, double ctrly,
        double x2, double y2) {
      setCurve(x1, y1, ctrlx, ctrly, x2, y2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getX1() {
      return x1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getY1() {
      return y1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getP1() {
      return new Point2D.Double(x1, y1);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlX() {
      return ctrlx;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlY() {
      return ctrly;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getCtrlPt() {
      return new Point2D.Double(ctrlx, ctrly);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getX2() {
      return x2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getY2() {
      return y2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getP2() {
      return new Point2D.Double(x2, y2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public void setCurve(double x1, double y1,
        double ctrlx, double ctrly,
        double x2, double y2) {
      this.x1 = x1;
      this.y1 = y1;
      this.ctrlx = ctrlx;
      this.ctrly = ctrly;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Rectangle2D getBounds2D() {
      double left = Math.min(Math.min(x1, x2), ctrlx);
      double top = Math.min(Math.min(y1, y2), ctrly);
      double right = Math.max(Math.max(x1, x2), ctrlx);
      double bottom = Math.max(Math.max(y1, y2), ctrly);
      return new Rectangle2D.Double(left, top,
          right - left, bottom - top);
    }

    /*
     * JDK 1.6 serialVersionUID
     */
    private static final long serialVersionUID = 4217149928428559721L;
  }

  /**
   * This is an abstract class that cannot be instantiated directly.
   * Type-specific implementation subclasses are available for
   * instantiation and provide a number of formats for storing
   * the information necessary to satisfy the various accessor
   * methods below.
   *
   * @see java.awt.geom.QuadCurve2D.Float
   * @see java.awt.geom.QuadCurve2D.Double
   * @since 1.2
   */
  protected QuadCurve2D() {
  }

  /**
   * Returns the X coordinate of the start point in
   * <code>double</code> in precision.
   *
   * @return the X coordinate of the start point.
   * @since 1.2
   */
  public abstract double getX1();

  /**
   * Returns the Y coordinate of the start point in
   * <code>double</code> precision.
   *
   * @return the Y coordinate of the start point.
   * @since 1.2
   */
  public abstract double getY1();

  /**
   * Returns the start point.
   *
   * @return a <code>Point2D</code> that is the start point of this <code>QuadCurve2D</code>.
   * @since 1.2
   */
  public abstract Point2D getP1();

  /**
   * Returns the X coordinate of the control point in
   * <code>double</code> precision.
   *
   * @return X coordinate the control point
   * @since 1.2
   */
  public abstract double getCtrlX();

  /**
   * Returns the Y coordinate of the control point in
   * <code>double</code> precision.
   *
   * @return the Y coordinate of the control point.
   * @since 1.2
   */
  public abstract double getCtrlY();

  /**
   * Returns the control point.
   *
   * @return a <code>Point2D</code> that is the control point of this <code>Point2D</code>.
   * @since 1.2
   */
  public abstract Point2D getCtrlPt();

  /**
   * Returns the X coordinate of the end point in
   * <code>double</code> precision.
   *
   * @return the x coordinate of the end point.
   * @since 1.2
   */
  public abstract double getX2();

  /**
   * Returns the Y coordinate of the end point in
   * <code>double</code> precision.
   *
   * @return the Y coordinate of the end point.
   * @since 1.2
   */
  public abstract double getY2();

  /**
   * Returns the end point.
   *
   * @return a <code>Point</code> object that is the end point of this <code>Point2D</code>.
   * @since 1.2
   */
  public abstract Point2D getP2();

  /**
   * Sets the location of the end points and control point of this curve
   * to the specified <code>double</code> coordinates.
   *
   * @param x1 the X coordinate of the start point
   * @param y1 the Y coordinate of the start point
   * @param ctrlx the X coordinate of the control point
   * @param ctrly the Y coordinate of the control point
   * @param x2 the X coordinate of the end point
   * @param y2 the Y coordinate of the end point
   * @since 1.2
   */
  public abstract void setCurve(double x1, double y1,
      double ctrlx, double ctrly,
      double x2, double y2);

  /**
   * Sets the location of the end points and control points of this
   * <code>QuadCurve2D</code> to the <code>double</code> coordinates at
   * the specified offset in the specified array.
   *
   * @param coords the array containing coordinate values
   * @param offset the index into the array from which to start getting the coordinate values and
   * assigning them to this <code>QuadCurve2D</code>
   * @since 1.2
   */
  public void setCurve(double[] coords, int offset) {
    setCurve(coords[offset + 0], coords[offset + 1],
        coords[offset + 2], coords[offset + 3],
        coords[offset + 4], coords[offset + 5]);
  }

  /**
   * Sets the location of the end points and control point of this
   * <code>QuadCurve2D</code> to the specified <code>Point2D</code>
   * coordinates.
   *
   * @param p1 the start point
   * @param cp the control point
   * @param p2 the end point
   * @since 1.2
   */
  public void setCurve(Point2D p1, Point2D cp, Point2D p2) {
    setCurve(p1.getX(), p1.getY(),
        cp.getX(), cp.getY(),
        p2.getX(), p2.getY());
  }

  /**
   * Sets the location of the end points and control points of this
   * <code>QuadCurve2D</code> to the coordinates of the
   * <code>Point2D</code> objects at the specified offset in
   * the specified array.
   *
   * @param pts an array containing <code>Point2D</code> that define coordinate values
   * @param offset the index into <code>pts</code> from which to start getting the coordinate values
   * and assigning them to this <code>QuadCurve2D</code>
   * @since 1.2
   */
  public void setCurve(Point2D[] pts, int offset) {
    setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
        pts[offset + 1].getX(), pts[offset + 1].getY(),
        pts[offset + 2].getX(), pts[offset + 2].getY());
  }

  /**
   * Sets the location of the end points and control point of this
   * <code>QuadCurve2D</code> to the same as those in the specified
   * <code>QuadCurve2D</code>.
   *
   * @param c the specified <code>QuadCurve2D</code>
   * @since 1.2
   */
  public void setCurve(QuadCurve2D c) {
    setCurve(c.getX1(), c.getY1(),
        c.getCtrlX(), c.getCtrlY(),
        c.getX2(), c.getY2());
  }

  /**
   * Returns the square of the flatness, or maximum distance of a
   * control point from the line connecting the end points, of the
   * quadratic curve specified by the indicated control points.
   *
   * @param x1 the X coordinate of the start point
   * @param y1 the Y coordinate of the start point
   * @param ctrlx the X coordinate of the control point
   * @param ctrly the Y coordinate of the control point
   * @param x2 the X coordinate of the end point
   * @param y2 the Y coordinate of the end point
   * @return the square of the flatness of the quadratic curve defined by the specified coordinates.
   * @since 1.2
   */
  public static double getFlatnessSq(double x1, double y1,
      double ctrlx, double ctrly,
      double x2, double y2) {
    return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly);
  }

  /**
   * Returns the flatness, or maximum distance of a
   * control point from the line connecting the end points, of the
   * quadratic curve specified by the indicated control points.
   *
   * @param x1 the X coordinate of the start point
   * @param y1 the Y coordinate of the start point
   * @param ctrlx the X coordinate of the control point
   * @param ctrly the Y coordinate of the control point
   * @param x2 the X coordinate of the end point
   * @param y2 the Y coordinate of the end point
   * @return the flatness of the quadratic curve defined by the specified coordinates.
   * @since 1.2
   */
  public static double getFlatness(double x1, double y1,
      double ctrlx, double ctrly,
      double x2, double y2) {
    return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly);
  }

  /**
   * Returns the square of the flatness, or maximum distance of a
   * control point from the line connecting the end points, of the
   * quadratic curve specified by the control points stored in the
   * indicated array at the indicated index.
   *
   * @param coords an array containing coordinate values
   * @param offset the index into <code>coords</code> from which to to start getting the values from
   * the array
   * @return the flatness of the quadratic curve that is defined by the values in the specified
   * array at the specified index.
   * @since 1.2
   */
  public static double getFlatnessSq(double coords[], int offset) {
    return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1],
        coords[offset + 4], coords[offset + 5],
        coords[offset + 2], coords[offset + 3]);
  }

  /**
   * Returns the flatness, or maximum distance of a
   * control point from the line connecting the end points, of the
   * quadratic curve specified by the control points stored in the
   * indicated array at the indicated index.
   *
   * @param coords an array containing coordinate values
   * @param offset the index into <code>coords</code> from which to start getting the coordinate
   * values
   * @return the flatness of a quadratic curve defined by the specified array at the specified
   * offset.
   * @since 1.2
   */
  public static double getFlatness(double coords[], int offset) {
    return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1],
        coords[offset + 4], coords[offset + 5],
        coords[offset + 2], coords[offset + 3]);
  }

  /**
   * Returns the square of the flatness, or maximum distance of a
   * control point from the line connecting the end points, of this
   * <code>QuadCurve2D</code>.
   *
   * @return the square of the flatness of this <code>QuadCurve2D</code>.
   * @since 1.2
   */
  public double getFlatnessSq() {
    return Line2D.ptSegDistSq(getX1(), getY1(),
        getX2(), getY2(),
        getCtrlX(), getCtrlY());
  }

  /**
   * Returns the flatness, or maximum distance of a
   * control point from the line connecting the end points, of this
   * <code>QuadCurve2D</code>.
   *
   * @return the flatness of this <code>QuadCurve2D</code>.
   * @since 1.2
   */
  public double getFlatness() {
    return Line2D.ptSegDist(getX1(), getY1(),
        getX2(), getY2(),
        getCtrlX(), getCtrlY());
  }

  /**
   * Subdivides this <code>QuadCurve2D</code> and stores the resulting
   * two subdivided curves into the <code>left</code> and
   * <code>right</code> curve parameters.
   * Either or both of the <code>left</code> and <code>right</code>
   * objects can be the same as this <code>QuadCurve2D</code> or
   * <code>null</code>.
   *
   * @param left the <code>QuadCurve2D</code> object for storing the left or first half of the
   * subdivided curve
   * @param right the <code>QuadCurve2D</code> object for storing the right or second half of the
   * subdivided curve
   * @since 1.2
   */
  public void subdivide(QuadCurve2D left, QuadCurve2D right) {
    subdivide(this, left, right);
  }

  /**
   * Subdivides the quadratic curve specified by the <code>src</code>
   * parameter and stores the resulting two subdivided curves into the
   * <code>left</code> and <code>right</code> curve parameters.
   * Either or both of the <code>left</code> and <code>right</code>
   * objects can be the same as the <code>src</code> object or
   * <code>null</code>.
   *
   * @param src the quadratic curve to be subdivided
   * @param left the <code>QuadCurve2D</code> object for storing the left or first half of the
   * subdivided curve
   * @param right the <code>QuadCurve2D</code> object for storing the right or second half of the
   * subdivided curve
   * @since 1.2
   */
  public static void subdivide(QuadCurve2D src,
      QuadCurve2D left,
      QuadCurve2D right) {
    double x1 = src.getX1();
    double y1 = src.getY1();
    double ctrlx = src.getCtrlX();
    double ctrly = src.getCtrlY();
    double x2 = src.getX2();
    double y2 = src.getY2();
    double ctrlx1 = (x1 + ctrlx) / 2.0;
    double ctrly1 = (y1 + ctrly) / 2.0;
    double ctrlx2 = (x2 + ctrlx) / 2.0;
    double ctrly2 = (y2 + ctrly) / 2.0;
    ctrlx = (ctrlx1 + ctrlx2) / 2.0;
    ctrly = (ctrly1 + ctrly2) / 2.0;
    if (left != null) {
      left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly);
    }
    if (right != null) {
      right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2);
    }
  }

  /**
   * Subdivides the quadratic curve specified by the coordinates
   * stored in the <code>src</code> array at indices
   * <code>srcoff</code> through <code>srcoff</code>&nbsp;+&nbsp;5
   * and stores the resulting two subdivided curves into the two
   * result arrays at the corresponding indices.
   * Either or both of the <code>left</code> and <code>right</code>
   * arrays can be <code>null</code> or a reference to the same array
   * and offset as the <code>src</code> array.
   * Note that the last point in the first subdivided curve is the
   * same as the first point in the second subdivided curve.  Thus,
   * it is possible to pass the same array for <code>left</code> and
   * <code>right</code> and to use offsets such that
   * <code>rightoff</code> equals <code>leftoff</code> + 4 in order
   * to avoid allocating extra storage for this common point.
   *
   * @param src the array holding the coordinates for the source curve
   * @param srcoff the offset into the array of the beginning of the the 6 source coordinates
   * @param left the array for storing the coordinates for the first half of the subdivided curve
   * @param leftoff the offset into the array of the beginning of the the 6 left coordinates
   * @param right the array for storing the coordinates for the second half of the subdivided curve
   * @param rightoff the offset into the array of the beginning of the the 6 right coordinates
   * @since 1.2
   */
  public static void subdivide(double src[], int srcoff,
      double left[], int leftoff,
      double right[], int rightoff) {
    double x1 = src[srcoff + 0];
    double y1 = src[srcoff + 1];
    double ctrlx = src[srcoff + 2];
    double ctrly = src[srcoff + 3];
    double x2 = src[srcoff + 4];
    double y2 = src[srcoff + 5];
    if (left != null) {
      left[leftoff + 0] = x1;
      left[leftoff + 1] = y1;
    }
    if (right != null) {
      right[rightoff + 4] = x2;
      right[rightoff + 5] = y2;
    }
    x1 = (x1 + ctrlx) / 2.0;
    y1 = (y1 + ctrly) / 2.0;
    x2 = (x2 + ctrlx) / 2.0;
    y2 = (y2 + ctrly) / 2.0;
    ctrlx = (x1 + x2) / 2.0;
    ctrly = (y1 + y2) / 2.0;
    if (left != null) {
      left[leftoff + 2] = x1;
      left[leftoff + 3] = y1;
      left[leftoff + 4] = ctrlx;
      left[leftoff + 5] = ctrly;
    }
    if (right != null) {
      right[rightoff + 0] = ctrlx;
      right[rightoff + 1] = ctrly;
      right[rightoff + 2] = x2;
      right[rightoff + 3] = y2;
    }
  }

  /**
   * Solves the quadratic whose coefficients are in the <code>eqn</code>
   * array and places the non-complex roots back into the same array,
   * returning the number of roots.  The quadratic solved is represented
   * by the equation:
   * <pre>
   *     eqn = {C, B, A};
   *     ax^2 + bx + c = 0
   * </pre>
   * A return value of <code>-1</code> is used to distinguish a constant
   * equation, which might be always 0 or never 0, from an equation that
   * has no zeroes.
   *
   * @param eqn the array that contains the quadratic coefficients
   * @return the number of roots, or <code>-1</code> if the equation is a constant
   * @since 1.2
   */
  public static int solveQuadratic(double eqn[]) {
    return solveQuadratic(eqn, eqn);
  }

  /**
   * Solves the quadratic whose coefficients are in the <code>eqn</code>
   * array and places the non-complex roots into the <code>res</code>
   * array, returning the number of roots.
   * The quadratic solved is represented by the equation:
   * <pre>
   *     eqn = {C, B, A};
   *     ax^2 + bx + c = 0
   * </pre>
   * A return value of <code>-1</code> is used to distinguish a constant
   * equation, which might be always 0 or never 0, from an equation that
   * has no zeroes.
   *
   * @param eqn the specified array of coefficients to use to solve the quadratic equation
   * @param res the array that contains the non-complex roots resulting from the solution of the
   * quadratic equation
   * @return the number of roots, or <code>-1</code> if the equation is a constant.
   * @since 1.3
   */
  public static int solveQuadratic(double eqn[], double res[]) {
    double a = eqn[2];
    double b = eqn[1];
    double c = eqn[0];
    int roots = 0;
    if (a == 0.0) {
      // The quadratic parabola has degenerated to a line.
      if (b == 0.0) {
        // The line has degenerated to a constant.
        return -1;
      }
      res[roots++] = -c / b;
    } else {
      // From Numerical Recipes, 5.6, Quadratic and Cubic Equations
      double d = b * b - 4.0 * a * c;
      if (d < 0.0) {
        // If d < 0.0, then there are no roots
        return 0;
      }
      d = Math.sqrt(d);
      // For accuracy, calculate one root using:
      //     (-b +/- d) / 2a
      // and the other using:
      //     2c / (-b +/- d)
      // Choose the sign of the +/- so that b+d gets larger in magnitude
      if (b < 0.0) {
        d = -d;
      }
      double q = (b + d) / -2.0;
      // We already tested a for being 0 above
      res[roots++] = q / a;
      if (q != 0.0) {
        res[roots++] = c / q;
      }
    }
    return roots;
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean contains(double x, double y) {

    double x1 = getX1();
    double y1 = getY1();
    double xc = getCtrlX();
    double yc = getCtrlY();
    double x2 = getX2();
    double y2 = getY2();

        /*
         * We have a convex shape bounded by quad curve Pc(t)
         * and ine Pl(t).
         *
         *     P1 = (x1, y1) - start point of curve
         *     P2 = (x2, y2) - end point of curve
         *     Pc = (xc, yc) - control point
         *
         *     Pq(t) = P1*(1 - t)^2 + 2*Pc*t*(1 - t) + P2*t^2 =
         *           = (P1 - 2*Pc + P2)*t^2 + 2*(Pc - P1)*t + P1
         *     Pl(t) = P1*(1 - t) + P2*t
         *     t = [0:1]
         *
         *     P = (x, y) - point of interest
         *
         * Let's look at second derivative of quad curve equation:
         *
         *     Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq''
         *     It's constant vector.
         *
         * Let's draw a line through P to be parallel to this
         * vector and find the intersection of the quad curve
         * and the line.
         *
         * Pq(t) is point of intersection if system of equations
         * below has the solution.
         *
         *     L(s) = P + Pq''*s == Pq(t)
         *     Pq''*s + (P - Pq(t)) == 0
         *
         *     | xq''*s + (x - xq(t)) == 0
         *     | yq''*s + (y - yq(t)) == 0
         *
         * This system has the solution if rank of its matrix equals to 1.
         * That is, determinant of the matrix should be zero.
         *
         *     (y - yq(t))*xq'' == (x - xq(t))*yq''
         *
         * Let's solve this equation with 't' variable.
         * Also let kx = x1 - 2*xc + x2
         *          ky = y1 - 2*yc + y2
         *
         *     t0q = (1/2)*((x - x1)*ky - (y - y1)*kx) /
         *                 ((xc - x1)*ky - (yc - y1)*kx)
         *
         * Let's do the same for our line Pl(t):
         *
         *     t0l = ((x - x1)*ky - (y - y1)*kx) /
         *           ((x2 - x1)*ky - (y2 - y1)*kx)
         *
         * It's easy to check that t0q == t0l. This fact means
         * we can compute t0 only one time.
         *
         * In case t0 < 0 or t0 > 1, we have an intersections outside
         * of shape bounds. So, P is definitely out of shape.
         *
         * In case t0 is inside [0:1], we should calculate Pq(t0)
         * and Pl(t0). We have three points for now, and all of them
         * lie on one line. So, we just need to detect, is our point
         * of interest between points of intersections or not.
         *
         * If the denominator in the t0q and t0l equations is
         * zero, then the points must be collinear and so the
         * curve is degenerate and encloses no area.  Thus the
         * result is false.
         */
    double kx = x1 - 2 * xc + x2;
    double ky = y1 - 2 * yc + y2;
    double dx = x - x1;
    double dy = y - y1;
    double dxl = x2 - x1;
    double dyl = y2 - y1;

    double t0 = (dx * ky - dy * kx) / (dxl * ky - dyl * kx);
    if (t0 < 0 || t0 > 1 || t0 != t0) {
      return false;
    }

    double xb = kx * t0 * t0 + 2 * (xc - x1) * t0 + x1;
    double yb = ky * t0 * t0 + 2 * (yc - y1) * t0 + y1;
    double xl = dxl * t0 + x1;
    double yl = dyl * t0 + y1;

    return (x >= xb && x < xl) ||
        (x >= xl && x < xb) ||
        (y >= yb && y < yl) ||
        (y >= yl && y < yb);
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean contains(Point2D p) {
    return contains(p.getX(), p.getY());
  }

  /**
   * Fill an array with the coefficients of the parametric equation
   * in t, ready for solving against val with solveQuadratic.
   * We currently have:
   * val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2
   * = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2
   * = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
   * 0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
   * 0 = C + Bt + At^2
   * C = C1 - val
   * B = 2*CP - 2*C1
   * A = C1 - 2*CP + C2
   */
  private static void fillEqn(double eqn[], double val,
      double c1, double cp, double c2) {
    eqn[0] = c1 - val;
    eqn[1] = cp + cp - c1 - c1;
    eqn[2] = c1 - cp - cp + c2;
    return;
  }

  /**
   * Evaluate the t values in the first num slots of the vals[] array
   * and place the evaluated values back into the same array.  Only
   * evaluate t values that are within the range &lt;0, 1&gt;, including
   * the 0 and 1 ends of the range iff the include0 or include1
   * booleans are true.  If an "inflection" equation is handed in,
   * then any points which represent a point of inflection for that
   * quadratic equation are also ignored.
   */
  private static int evalQuadratic(double vals[], int num,
      boolean include0,
      boolean include1,
      double inflect[],
      double c1, double ctrl, double c2) {
    int j = 0;
    for (int i = 0; i < num; i++) {
      double t = vals[i];
      if ((include0 ? t >= 0 : t > 0) &&
          (include1 ? t <= 1 : t < 1) &&
          (inflect == null ||
              inflect[1] + 2 * inflect[2] * t != 0)) {
        double u = 1 - t;
        vals[j++] = c1 * u * u + 2 * ctrl * t * u + c2 * t * t;
      }
    }
    return j;
  }

  private static final int BELOW = -2;
  private static final int LOWEDGE = -1;
  private static final int INSIDE = 0;
  private static final int HIGHEDGE = 1;
  private static final int ABOVE = 2;

  /**
   * Determine where coord lies with respect to the range from
   * low to high.  It is assumed that low &lt;= high.  The return
   * value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
   * or ABOVE.
   */
  private static int getTag(double coord, double low, double high) {
    if (coord <= low) {
      return (coord < low ? BELOW : LOWEDGE);
    }
    if (coord >= high) {
      return (coord > high ? ABOVE : HIGHEDGE);
    }
    return INSIDE;
  }

  /**
   * Determine if the pttag represents a coordinate that is already
   * in its test range, or is on the border with either of the two
   * opttags representing another coordinate that is "towards the
   * inside" of that test range.  In other words, are either of the
   * two "opt" points "drawing the pt inward"?
   */
  private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
    switch (pttag) {
      case BELOW:
      case ABOVE:
      default:
        return false;
      case LOWEDGE:
        return (opt1tag >= INSIDE || opt2tag >= INSIDE);
      case INSIDE:
        return true;
      case HIGHEDGE:
        return (opt1tag <= INSIDE || opt2tag <= INSIDE);
    }
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean intersects(double x, double y, double w, double h) {
    // Trivially reject non-existant rectangles
    if (w <= 0 || h <= 0) {
      return false;
    }

    // Trivially accept if either endpoint is inside the rectangle
    // (not on its border since it may end there and not go inside)
    // Record where they lie with respect to the rectangle.
    //     -1 => left, 0 => inside, 1 => right
    double x1 = getX1();
    double y1 = getY1();
    int x1tag = getTag(x1, x, x + w);
    int y1tag = getTag(y1, y, y + h);
    if (x1tag == INSIDE && y1tag == INSIDE) {
      return true;
    }
    double x2 = getX2();
    double y2 = getY2();
    int x2tag = getTag(x2, x, x + w);
    int y2tag = getTag(y2, y, y + h);
    if (x2tag == INSIDE && y2tag == INSIDE) {
      return true;
    }
    double ctrlx = getCtrlX();
    double ctrly = getCtrlY();
    int ctrlxtag = getTag(ctrlx, x, x + w);
    int ctrlytag = getTag(ctrly, y, y + h);

    // Trivially reject if all points are entirely to one side of
    // the rectangle.
    if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) {
      return false;       // All points left
    }
    if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) {
      return false;       // All points above
    }
    if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) {
      return false;       // All points right
    }
    if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) {
      return false;       // All points below
    }

    // Test for endpoints on the edge where either the segment
    // or the curve is headed "inwards" from them
    // Note: These tests are a superset of the fast endpoint tests
    //       above and thus repeat those tests, but take more time
    //       and cover more cases
    if (inwards(x1tag, x2tag, ctrlxtag) &&
        inwards(y1tag, y2tag, ctrlytag)) {
      // First endpoint on border with either edge moving inside
      return true;
    }
    if (inwards(x2tag, x1tag, ctrlxtag) &&
        inwards(y2tag, y1tag, ctrlytag)) {
      // Second endpoint on border with either edge moving inside
      return true;
    }

    // Trivially accept if endpoints span directly across the rectangle
    boolean xoverlap = (x1tag * x2tag <= 0);
    boolean yoverlap = (y1tag * y2tag <= 0);
    if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
      return true;
    }
    if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
      return true;
    }

    // We now know that both endpoints are outside the rectangle
    // but the 3 points are not all on one side of the rectangle.
    // Therefore the curve cannot be contained inside the rectangle,
    // but the rectangle might be contained inside the curve, or
    // the curve might intersect the boundary of the rectangle.

    double[] eqn = new double[3];
    double[] res = new double[3];
    if (!yoverlap) {
      // Both Y coordinates for the closing segment are above or
      // below the rectangle which means that we can only intersect
      // if the curve crosses the top (or bottom) of the rectangle
      // in more than one place and if those crossing locations
      // span the horizontal range of the rectangle.
      fillEqn(eqn, (y1tag < INSIDE ? y : y + h), y1, ctrly, y2);
      return (solveQuadratic(eqn, res) == 2 &&
          evalQuadratic(res, 2, true, true, null,
              x1, ctrlx, x2) == 2 &&
          getTag(res[0], x, x + w) * getTag(res[1], x, x + w) <= 0);
    }

    // Y ranges overlap.  Now we examine the X ranges
    if (!xoverlap) {
      // Both X coordinates for the closing segment are left of
      // or right of the rectangle which means that we can only
      // intersect if the curve crosses the left (or right) edge
      // of the rectangle in more than one place and if those
      // crossing locations span the vertical range of the rectangle.
      fillEqn(eqn, (x1tag < INSIDE ? x : x + w), x1, ctrlx, x2);
      return (solveQuadratic(eqn, res) == 2 &&
          evalQuadratic(res, 2, true, true, null,
              y1, ctrly, y2) == 2 &&
          getTag(res[0], y, y + h) * getTag(res[1], y, y + h) <= 0);
    }

    // The X and Y ranges of the endpoints overlap the X and Y
    // ranges of the rectangle, now find out how the endpoint
    // line segment intersects the Y range of the rectangle
    double dx = x2 - x1;
    double dy = y2 - y1;
    double k = y2 * x1 - x2 * y1;
    int c1tag, c2tag;
    if (y1tag == INSIDE) {
      c1tag = x1tag;
    } else {
      c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y + h)) / dy, x, x + w);
    }
    if (y2tag == INSIDE) {
      c2tag = x2tag;
    } else {
      c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y + h)) / dy, x, x + w);
    }
    // If the part of the line segment that intersects the Y range
    // of the rectangle crosses it horizontally - trivially accept
    if (c1tag * c2tag <= 0) {
      return true;
    }

    // Now we know that both the X and Y ranges intersect and that
    // the endpoint line segment does not directly cross the rectangle.
    //
    // We can almost treat this case like one of the cases above
    // where both endpoints are to one side, except that we will
    // only get one intersection of the curve with the vertical
    // side of the rectangle.  This is because the endpoint segment
    // accounts for the other intersection.
    //
    // (Remember there is overlap in both the X and Y ranges which
    //  means that the segment must cross at least one vertical edge
    //  of the rectangle - in particular, the "near vertical side" -
    //  leaving only one intersection for the curve.)
    //
    // Now we calculate the y tags of the two intersections on the
    // "near vertical side" of the rectangle.  We will have one with
    // the endpoint segment, and one with the curve.  If those two
    // vertical intersections overlap the Y range of the rectangle,
    // we have an intersection.  Otherwise, we don't.

    // c1tag = vertical intersection class of the endpoint segment
    //
    // Choose the y tag of the endpoint that was not on the same
    // side of the rectangle as the subsegment calculated above.
    // Note that we can "steal" the existing Y tag of that endpoint
    // since it will be provably the same as the vertical intersection.
    c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);

    // c2tag = vertical intersection class of the curve
    //
    // We have to calculate this one the straightforward way.
    // Note that the c2tag can still tell us which vertical edge
    // to test against.
    fillEqn(eqn, (c2tag < INSIDE ? x : x + w), x1, ctrlx, x2);
    int num = solveQuadratic(eqn, res);

    // Note: We should be able to assert(num == 2); since the
    // X range "crosses" (not touches) the vertical boundary,
    // but we pass num to evalQuadratic for completeness.
    evalQuadratic(res, num, true, true, null, y1, ctrly, y2);

    // Note: We can assert(num evals == 1); since one of the
    // 2 crossings will be out of the [0,1] range.
    c2tag = getTag(res[0], y, y + h);

    // Finally, we have an intersection if the two crossings
    // overlap the Y range of the rectangle.
    return (c1tag * c2tag <= 0);
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean intersects(Rectangle2D r) {
    return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean contains(double x, double y, double w, double h) {
    if (w <= 0 || h <= 0) {
      return false;
    }
    // Assertion: Quadratic curves closed by connecting their
    // endpoints are always convex.
    return (contains(x, y) &&
        contains(x + w, y) &&
        contains(x + w, y + h) &&
        contains(x, y + h));
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean contains(Rectangle2D r) {
    return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public Rectangle getBounds() {
    return getBounds2D().getBounds();
  }

  /**
   * Returns an iteration object that defines the boundary of the
   * shape of this <code>QuadCurve2D</code>.
   * The iterator for this class is not multi-threaded safe,
   * which means that this <code>QuadCurve2D</code> class does not
   * guarantee that modifications to the geometry of this
   * <code>QuadCurve2D</code> object do not affect any iterations of
   * that geometry that are already in process.
   *
   * @param at an optional {@link AffineTransform} to apply to the shape boundary
   * @return a {@link PathIterator} object that defines the boundary of the shape.
   * @since 1.2
   */
  public PathIterator getPathIterator(AffineTransform at) {
    return new QuadIterator(this, at);
  }

  /**
   * Returns an iteration object that defines the boundary of the
   * flattened shape of this <code>QuadCurve2D</code>.
   * The iterator for this class is not multi-threaded safe,
   * which means that this <code>QuadCurve2D</code> class does not
   * guarantee that modifications to the geometry of this
   * <code>QuadCurve2D</code> object do not affect any iterations of
   * that geometry that are already in process.
   *
   * @param at an optional <code>AffineTransform</code> to apply to the boundary of the shape
   * @param flatness the maximum distance that the control points for a subdivided curve can be with
   * respect to a line connecting the end points of this curve before this curve is replaced by a
   * straight line connecting the end points.
   * @return a <code>PathIterator</code> object that defines the flattened boundary of the shape.
   * @since 1.2
   */
  public PathIterator getPathIterator(AffineTransform at, double flatness) {
    return new FlatteningPathIterator(getPathIterator(at), flatness);
  }

  /**
   * Creates a new object of the same class and with the same contents
   * as this object.
   *
   * @return a clone of this instance.
   * @throws OutOfMemoryError if there is not enough memory.
   * @see java.lang.Cloneable
   * @since 1.2
   */
  public Object clone() {
    try {
      return super.clone();
    } catch (CloneNotSupportedException e) {
      // this shouldn't happen, since we are Cloneable
      throw new InternalError(e);
    }
  }
}
